Programmed digital-computer-controlled system for automatic growth of semiconductor crystals

ABSTRACT

A Czochralski crystal puller is automatically controlled by a specially programmed digital computer to produce constant diameter, high-quality semiconductor crystals. Provision is made in the programming of the computer for the solution of partly theoretical and partly empirical mathematical models for simultaneously controlling heater temperature, crystal lift rate, crucible lift rate, crystal rotation rate and crucible rotation rate. Computer solutions of the equations are made in real time and the computer is an online integral component of the overall crystal growth system. The mathematical models concerned with heater temperature control and crystal lift control include data extrapolation for the anticipatory control of crystal diameter to compensate for the low dynamic response of the Czochralski crystal puller to changes in the heater control signals.

United States Patent inventors Appl. No.

Filed Patented Assignee PROGRAMMED DIGITAL-COMPUTER- CONTROLLED SYSTEM FOR AUTOMATIC GROWTH OF SEMICONDUCTOR CRYSTALS 3 Claims, 5 Drawing Figs.

[1.8. CI 235/150, 235/151. l2, 23/295 Int. Cl G06i 15/46, 606i 9/06 Field of Search 235/150.

[56] References Cited UNITED STATES PATENTS 3,246,550 4/1966 Galey et al 83/56 Primary ExaminerMalcolm A. Morrison Assistant Examiner-Edward 1. Wise Anorneys--Hanifin and .lancin and Robert J. Haase ABSTRACT: A Czochralski crystal puller is automatically controlled by a specially programmed digital computer to produce constant diameter, high-quality semiconductor crystals. Provision is made in the programming of the computer for the solution of partly theoretical and partly empirical mathematical models for simultaneously controlling heater temperature, crystal lift rate, crucible lift rate, crystal rotation rate and crucible rotation rate. Computer solutions of the equations are made in real time and the computer is an online integral component of the overall crystal growth system. The mathematical models concerned with heater temperature control and crystal lift control include data extrapolation for the anticipatory control of crystal diameter to compensate for the low dynamic response of the Czochralski crystal puller to changes in the heater control signals.

COMPUTER CONTROL SYSTEM SEED CARL R. VALENTINO M 2 U C H! i H! o w 8 w m WN F REA N W D K II 0 m mm NH DR llll NE DR T% R.

SHEEI 1 OF 4 COMPUTER CONTROL SYSTEM BY ATTORNEY H PAIENTEUunv 1s l97l RADIATION SENSOR 7 Q PAIENTEuunv 1619" 3.621 .213

sum 2 or 4 3 SELECT CRYSTAL TYPE A DIAMETER 52 ACCESS DATA TABLE FOR PULL SPEED A ROTATION SPEEDS 33 ACCE ATA TA FOR EHPI HEAT CONTROL A SPEED CONTROL CONSTANTS 34 START PULL.

E INITIAL HEAT POINT. CHANGE PULL SPEED SET POINT FROM 0 55 PREDETERMINED PULL D.

INCREMENT PROCESS TIME EF 'L; 55

READ SENSOR s1 VIA PROCESS INTERRUPT Q P &STORE m COMMUN|CAT|ON""' SENSOR 31 READING mom AREA \38 k 59 I 40 T..M LLLL L E NEOK- TN POWER ORA LY INC E XTAL A CRU LIFT SPEEDS D ON PREDETERNINED CONSTANT INCREMENTS APATENTEDIHV 16 I9?! SHEET 3 0F 4 HEE FIG. 4

CALCULATE CRYSTAL LENGTH BASED ON PULL SPEED H TTHE mcHEHEHT \58 v 57 EXECUTE VIITHDRAWAL PHASE To PROVIDE PREDETERNINED INCREMENTAL CHANGES OF ALL sET POINTS cuRvE FTT PAST SENSOR 3i READINGS T PROJECT NEW SENSOR 31 READING \45 CALCULATE HEAT CHANGE BASED ON IDEALIZED EQUATION HT 46 MODIFY HEAT CHANGE BASED ON OOMPENSATING v\ EQUATION 2) 47 CALCULATE NEW PULL SPEED BASED ON EQUATION (3) CALCULATE TOTAL MELT DROP TO 51 FIG. 5

PATENTEMuv I6 I97! 3, 6 21 .2 l 3 saw u or 4 FROM 50 FIG. 4

F I G. 5

IS MELT SURFACE IN OURVED DRUCIBLE YES CALCULATE DIGITAL FROM 41 HEATER POWER VALUE 3 BASED ON EQUATION 5) 42 TO DIGITAL -TO- ANALOG CONVERTER CALCULATE OUTPUT T0 NOTOR BASED ON EQUATION (9) TO OIGITAL-TO-ANALOG CONVERTER READ AND STORE HEATER TENP XTAL PULL SPEED CRUCIBLE LIFT SPEED XTAL ROTATION SPEED 55 CRUCIBLE ROTATION SPEED T0 37 HOS BACKGROUND OF THE INVENTION The Czochralski method of crystal growth. as used in the fabrication of silicon and germanium single crystals, heretofore has been recognized to be an art, i.e., highly skilled operators have been required to maintain a reasonably high yield of quality product. As is well known, the Czochralski technique is a method of growing single crystals, oriented in a specified crystallographic direction, from a mass of molten raw materials. To achieve the desired electrical characteristics for the crystal, a predetermined amount of an impurity element, called dopant, is introduced into the melt. A seed of single crystal oriented in the desired crystallographic direction is then inserted into the melt and allowed to propagate by careful adjustment of the growth conditions including melt temperature, crystal lift rate, crucible lift rate, crystal rotation rate,'crucible rotation rate and gas flow rate. Modifications of the crystal growth parameters cause variations in the resultant product. For example, crystal diameter can be varied by changes in the temperature of the melt or by changes of the growth rate. Crystal resistivity can also be altered by changes of temperature or growth rates, while variation of the radial resistivity can be realized by change of the crystal and crucible rotation parameters.

New progress is being made constantly in crystal growing. Larger crystals are being grown, the growth speed is being increased, new materials are being used, and more stringent electrical characteristics are desired to be achieved. The time has come where the capabilities of even the most skilled operator are being taxed toward the limit and beyond.

In the prior art manual technique of crystal pulling, the operator observes the crystal growth at a distance of about a foot through a viewing port in the furnace housing. The operator must judge the crystal diameter size from sight and make the necessary adjustments on the crystal puller control panel.

' He has'no precise instructions onhow to make the adjustments. The operator learns his skills from written operating procedures and on-the-job'training. Learning by doing is truly the only way the skill is learned. Thus, the human factor is always present in the control loop. No matter how careful a manual operator may be in making heater and speed adjustments, he lacks precise reference points and can easily initiate crystal dislocations due to thermal and mechanical shock caused by excessive or rapid changes of control parameters.

SUMMARY OF THE INVENTION In accordance with the present invention, crystal diameter is sensed, for example, by an optical pyrometer, each time that the growing crystal is rotated to a predetermined angular position. The diameter pyrometer readings are curve fitted and extrapolated to predict the crystal diameter at a projected time. A second optical pyrometer continuously measures the temperature of the melt in the crucible. The melt temperature pyrometer reading is modified by an equation which takesinto account the continuous change in furnace thermal characteristics caused by crucible lift ,and melt depletion. The modified melt temperature reading is theoretically correct but suffers from error to the extent that uncontrolled thermal instabilities are present which I affect crystal diameter. Accordingly, the present invention provides for a correction factor using the extrapolated crystal diameter previously mentioned. The resulting corrected melt temperature is compared with the actual measured melt temperature pyrometer reading and the power input to the crucible heater is adjusted if a difference between the corrected melt temperature and the actual melt temperature is indicated.

Crystal lift (pull) control is accomplished in a somewhat similar manner. A predetermined nominal crystal lift speed term is mathematicallymodified utilizing extrapolated crystal diameter values to yield a corrected lift speed term. The corrected lift speed term then is compared to actual measured crystal lift speed to provide closed-loop servocontrol of the crystal lift motor. Provision is also made for the control of crystal and crucible rotation as well as crucible lift speed. In the disclosed preferred embodiment, the aforementioned crystal-growing process parameters are controlled by a specially programmed general purpose online digital computer.

BRIEF DESCRIPTION OF THE DRAWING FIG. I is a simplified schematic representation of the spe cially programmed digital computer control system and the crystal puller utilized in the preferred embodiment of the present invention;

FIG. 2 is a simplified sketch of atypical crystal grown in accordance with the present invention; and

FIGS. 3, 4 and 5 together comprise a high-level flow chart representation of the computer program utilized in the embodiment of FIG. 1.

DESCRIPTION OF THE PREFERRED EMBODIMENT As is well known, the Czochralski method is used for growing single-structured crystals from a silicon melt. In an illustrative case, a silicon charge of 1,000 grams is melted in a Quartz crucible in a furnace and maintained at a temperature slightly above l,400 C. An airtight cylindrical chamber and a crystal lift mechanism are integrally mounted on the furnace. A small single crystal seed is lowered in the chamber, dipped into the surface of the melt, and then slowly withdrawn. The melt solidifies on the seed as it is withdrawn, creating a single crystal. The seed crystal and the crucible are rotated while the crystal is being pulled. The rotation stirs the melt effectively and eliminates undesired temperature gradients which result in asymmetrical crystal growth. Stirring also increases the homogeneity of the silicon dopant mixture which improves the electrical characteristics of the crystal. The crucible elevation is adjustable. Withdrawal of the crystal reduces the remaining melt volume and lowers the solid-liquid interface level. In order 'to maintain the interface level in the center of the isothermal region of the heater, the crucible is slowly adjusted upward to compensate for the lowering of the interface level. Thus, the crucible is raised continuously in relation to the fixed position of the heater.

The basic components of the conventional Czochralski crystal puller just described are shown in FIG. I. Seed 1 is lifted and rotated relative to melt 2 by shaft 3. Crucible 4 which contains melt 2 is lifted and rotated by hollow shaft 5. Shaft 3 is lifted and rotated by motors 6 and 7, respectively. Shaft 5 is similarly controlled by motors 8 and 9. A partially grown crystal 10 is shown between seed 1 and the surface of melt 2. The temperature of melt 2 is in part controlled by heater ll.

In the computer control system of the present invention, certain process parameter values are predetermined (preset by the operator) while others are measured during the actual growing process. Predetermined values preset by the operator include the desired crystal diameter, the type of crystal to be grown, the weight of the silicon charge in the crucible, the

. nominal pull speed desired, and the diameter of the seed to be used. The parameter values which are measured during the actual growth of the crystal include seed lift and rotation, crucible lift and rotation, the diameter of the growing crystal, and the temperature of the melt in the crucible. The crystal-growing process parameters which are controlled by the computer in real time include seed lift and rotation, crucible lift and rotation, and melt temperature. Referring to FIG. 1, computer control system I2 receives signals on lines 13 through 18, inclusive, representing real time measured values of seed rotation, seed lift, crystal diameter, crucible rotation, crucible lift, and melt temperature, respectively. Computer control system 12, in turn, provides real time control signals on lines 19 through 23, inclusive, for determining crystal rotation, crystal lift, crucible rotation, crucible lift, and heater power, respectively. A viewing port 24 is provided in the side of the crystalgrowing chamber 25 for operator observation of melt 2.

Computer control system 12 preferably is a conventional programmable process control digital computer such as, for example. the IBM l7l0 or 1800 process control computer. Computer control system 12 also includes the usual conventional interface instrumentation for gathering information on the crystal-growing process parameters in the form of electrical analog signals from the motor tachometers 26 through 29, inclusive, and from radiation sensor 30 which senses the temperature of the melt 2 at the bottom of crucible 4 via the ho]- low shaft 5. Analog to digital converters transform the analog signals into equivalent digital representations. Computer control system 12 further includes units for controlling the speeds of motors 6 through 9, inclusive, and a magnetic amplifier for driving furnace heater 11. A manual data entry unit within control system 12 allows for the insertion of data by the operator at the start of the growing process as will be described later.

in accordance with the present method, special programming is provided for computer control system 12 for producing constant diameter, high-quality semiconductor crystals. More specifically, the programming produces an online control mechanism uniquely equipped for executing control of predetermined process parameters in accordance with special mathematical models. For example, melt temperature control is based in part upon a first mathematical model describing the heat energy flow into and out of an idealized crystal puller (having no uncontrolled crystal-growing process variables) and in part upon a second mathematical model which compensates the idealized model for the uncontrolled parameters which are unavoidably present in the physically realizable system. It has been found that optimum results are not achieved using either the idealized model or the compensating model alone for controlling the process variables. However, when both models are used concurrently in real time computation within an online computer process control system in accordance with the present invention, very significant and reproducible improvements in the grown crystal are achieved. A somewhat similar philosophy is utilized in controlling the speed of motor 6 which determines the crystal pull rate. Less sophisticated control techniques are adequate for the remaining process parameters, i.e., crystal rotation, crucible rotation, and crucible lift speed.

The crystal-growing process customarily is divided into four main portions. Starting with a small single crystal seed which is dipped into the melt and then slowly withdrawn to allow the melt to solidify on the seed as it is withdrawn, the crystal growth conditions are adjusted to produce the neck-in, roundover, main body, and sprout portions of the crystal as presented in FlG. 2. During the neck-in phase or initial growth of the crystal from the seed to the crystal shoulder, the seed diameter is first reduced and then increased in order to assure dislocation-free growth as is well understood in the art. Heater power is first increased and then decreased to produce the decreasing and increasing portions, respectively, of the growing crystal. The amount of heat change is precalculated and stored in the computer and is parceled out in terms of incremental power changes at predetermined process time increments. All other controlled process variables are maintained constant. There is no process parameter feedback to the computer during the neck-in phase.

The transition between the neck-in and the main body growth phases is termed round-over. Round-over starts as soon as the signal on line 15 of FIG. 1 indicates that the growing crystal is approaching the desired diameter. Round-over is accomplished by incrementing the crystal lift speed and the crucible lift speed gradually to their respective main body growth values while heater power input is increased to stop the expansion of the crystal diameter.

Diameter control during the main body growth phase is accomplished with the aid of the idealized and the compensating mathematical models previously discussed in connection with heater power and crystal lift control by the computer. Crystal rotation and crucible rotation preferably are maintained constant but it is necessary to vary the crucible lift speed to maintain the solid-liquid interface level of the melt at the same location relative to heater ll of FIG. 1 despite the loss of the melt as the growing crystal solidifies.

The maintenance of the solid-liquid interface level at a fixed point within the temperature profile of the heater ll makes for more accurate control of the critical solid-liquid interface temperature and also presents a fixed target distance for the radiation sensor 31 of FIG. 1. Sensor 31 is aimed at the solidliquid interface of the growing crystal and responds to changes in crystal diameter in the manner described in copending US. Pat. application Ser. No. 530,819 filed Mar. 1, l966, for Control System in the names of Ralph G. Dessauer, Eugene J. Patzner and Michael R. Poponiak. The output signal provided by sensor 31 would not be a reliable indication of crystal diameter in the event that the optical path length between it and the solid-liquid interface were allowed to vary in an uncontrolled manner. Crucible lift speed control is based upon the predetermined nominal crystal pull speed value and a computation of the melt depletion at successive process time increments as the crystal is growing. Provision is made for modifying the computation depending on whether the surface of the melt is within the cylindrical portion of the crucible or has been lowered to the curved portion at the bottom of the crucible.

The sprout portion of the crystal is formed when the supply of the melt is nearing exhaustion by maintaining a nominal pull speed while gradually reducing crucible lift speed to zero, gradually reducing crystal rotation to half its value during the main body growth phase and by gradually increasing heater power input at a predetermined rate.

It was found in one typical embodiment of the present invention that during the main body growth of the semiconductor crystal the increment of heater power that must be supplied during a given process time increment to take into account the changed position of crucible 4 relative to heater 11 (due to the incremental lift of crucible 4 during the same time increment) less the heat of fusion released upon the solidification of the growing crystal can be represented by the following idealized equation:

dR 1 was where AR heater power increment expressed as an equivalent reading on sensor 30 of FIG. l

(.= crucible position relative to heater ll A! time interval between two consecutive readings of sensor 30 made during two consecutive process time intervals H,= heat of fusionfreed, B.t.u. per unit of time F,, millivolt reading change of sensor 30 per kw. of heat power change (2 mv./kw. is used for F], in a typical instance) F, empirical factor in the range from 0.07 to 0.04, determined by the amount of heat removed by the argon gas flow u heater efficiency (-95 percent) The heater power increment AR resulting from the above idealized equation must be compensated to reduce crystal diameter variations caused by crystal puller system thermal instabilities which are not taken into account by the idealized equation. Further, the required compensation should be based upon a forward projection in time in order to allow for the very substantial thermal lag in the crystal puller between the time that heater power is adjusted and the time that the temperature of the melt responds to the adjustment. ln accordance with the present invention, the idealized heat increment term is compensated in accordance with the following ARI adjusted mine alrequlred Increment cleaner 8') rrmlinu mar.) AR required increment of sensor 30 reading calculated by equation l) I projected reading of sensor 31 I reference reading of sensor 31 (preselected at a point of high sensitivity to changes in temperature) I reading of sensior 31 during the current process time interval Irv reading of sensor 31 during the immediately preceding process time interval f] proportional factor 0.02 (typical value) f, damping factor 0.06 (typical value) f, scale factor 0.20 (typical value) The thermal lag problem is further reduced by adjusting crystal pull speed in addition .to the above-described heater power adjustment to achieve the fastest crystal diameter response to a given computer command. A nominal pull speed is selected by the computer from a stored table of values at the start of the computer-controlled growing process based upon crystal type and desired diameter data supplied by the operator. The speed nominal value is based upon an idealized crystal-growing system in which there are no uncontrolled variables. Unlike the idealized heater power adjustment previously discussed which must be continuously computed due to changes in the thermal system predicted by the idealized heat balance equation (l), the nominal pull speed is a constant value that is predetermined and stored in the computer memory. As in the case of the heater power adjustment, however, it is necessary to compensate the nominal pull speed term for growth process instabilities affecting the diameter of the growing crystal. The nominal value of the pull speed is adjusted in accordance with the following equation:

X P new pull speed X P,- nominal pull speed 1} proportion factor 1.0 (typical value) f dampening factor 4.0 (typical value) I, I I and ate defined as in equation (2) A prime example of a crystal growth process instability which requires that the nominal heater power increment and nominal pull speed be compensated so as to exercise close diameter control of the growing crystal is due to the formation offluff on the internal furnace walls. The fluff is caused by a reaction of the silicon melt with the Quartz crucible holding the melt at crystal-growing temperatures. The silicon monoxide or fluff" is produced in a vapor state but condenses on the relatively cool surfaces of the furnace walls. Fluff can build up heavily on the walls and, because of its thermal insulative properties, cause instability of the heat balance. Consequently both the conductive and reflective qualities of the furnace walls are changed. This directly affects the melt temperature and the growth of the crystal diameter.

Although the present invention can be practiced with the aid of analog computing apparatus, it is preferred at the present state of the art to exploit the greater speed and accuracy of the programmable general purpose digital computer such as, for example, the IBM 1710 or 1800 process control computer. A preferred program for instrumenting said digital computer in accordance with the present invention represented in the high-level flow chart of FIGS. 3, 4 and 5. The flow chart comprises a number of functional blocks and decisional blocks representing respective computer operations. Standard programming techniques, forming'no part of the present invention, can be employed to reduce the highlevel flow chart of FIGS. 3, 4 and 5 into equivalent machine language instructions in a known manner. It will be recognized, of course, that only the process-oriented portion ofthe overall program is represented by FIGS. 3, 4 and 5. in addition, there is to be provided the customary system software including machine control, housekeeping, job-organizing, program-loading, and language-translating programs. Such system software is well known and is not required for an understanding of the present invention.

Block 32 of FIG. 3 represents the data input provided to the computer by the operator, namely crystal type and diameter. Blocks 33 and 34 represent the computer initialization program during which the computer accesses (block 33) a data table and selects nominal values for crystal pull speed, crystal rotation speed and crucible rotation speed corresponding in a predetermined manner to the crystal type and diameter selected by the operator in block 32. The computer next accesses (block 34) a second data table and selects empirically determined heat control and speed control constants utilized in the neck-in and round-over phases of the crystal growing process. All of the selected data is transferred to the communication area of the computer memory for ready access when needed for subsequent computations. At this point, the computer-controlled crystal-growing process is ready to begin upon the initiation of an operator signal indicating that the melt is at the proper temperature.

Complete computer automation of the crystal-growing process is handicapped by the lack of an adequate device for sensing the absolute temperature value of the solid-liquid interface (heat-of-fusion ring) and the temperature distribution in the melt. It is preferable to rely on the operators estimate or judgment as to when the temperature of the melt is correct for the initiation of the crystal-growing process. This judgment is made, as in the prior art manual crystal-pulling processes, by checking the reading of radiation sensor 30 of FIG. 1 while observing the appearance of the seed-melt interface through viewing port 24. When the operator judges that the proper temperature is present, he pushes a start button and initiates computer control of the process. Provision preferably is made also for allowing the operator to override computer control during the neck-in and round-over phases of the crystal growth. For example, if he observes that said portions are not proceeding satisfactorily, he may add to or subtract from the preset heater power increments generated by the computer during said phases.

When the operator pushes the start button (block 36), the computer automatically senses and records the temperature represented by the output signal from radiation sensor 30 of FIG. 1 at that time. At the same time, the seed is withdrawn from the melt at a predetermined rate. For example, the seedpulling rate may be increased from 0 to 2.7 inches per hour. At preset process time intervals, e.g. every l8 seconds, the computer generates new set points for heater power control and for crystal and crucible lift and rotation control. Block 37 of FIG. 3 represents that portion of the computer program which measures oh and keeps track of the computer process time increments.

At each process time interval, the computer accesses(bl0ck 38) the memory location at which the signals from radiation sensor 31 are stored. It is important that the signals from sensor 31 (representing the diameter of the rotating crystal 10) be stored only at those times when the rotating crystal assumes a predetermined angular position. This can be readily accomplished by providing a simple cam-actuated switch (not shown) which samples the signals on line 15 from sensor 31 each time that rotating shaft 3 reaches a predetermined angle. Provision is made for interrupting the computer process irrespective of the computations then underway each time that the switch is actuated. The process interrupt reading and storage of the crystal diameter data represented by the signal from optical sensor 31 is represented by block 39 of F 1G. 3.

Each time that the computer accesses the memory location where the diameter data from sensor 31 are stored, a decision is madeas to whether the crystal is nearing its desired nominal diameter value. This decision is represented by block 40. In the event that the crystal is not yet out to the full diameter desired, the crystal is still within the neck-in phase and an appropriate heater power increment signal must be generated for application to heater ll of FIG. 1 during the next process time increment. The heater power increment is calculated (block 41) for each of the process time increments with the aid of the following empirically determined relationship:

where A change of angle of growth (degrees) desired for a given process time increment P percent power change required expressed as a reading in millivolts of sensor 30 I" =empirical factor 1.051 (typical value) F factor 0.201 (typical value) The initial heat set point (block 36) which was stored when the operator pushbutton was depressed, is incremented to a slightly different value in accordance with the computation of block 41 in the event that a decision is made (block 40) that the crystal diameter is not yet at its desired size. The incremented set point is inserted into the following equation to compute (block 42 of FIG. 5) the value m,, which is the digital representation of the electrical power to be applied to heater 11. The value (m,,) is made available to a digital-to-analog converter which interfaces the computer per se and the analog drive circuits (also within computer control system 12) for heater l1.

where m,, digital output to heater m, a digital reference power value for heat furnace control. It is a function of the heater element in use and its range typically is 400 to 600 units K rate factor 2.5 (typical value) K power factor 4.0 (typical value) K base adjustment factor 0.3 (has the sign of the term V nth reading of sensor 30 S value of set point at V,

e error value the neck-in Returning to decision block 40 of FIG. 3, eventually the output signal produced by radiation detector 31 will indicate that the crystal diameter is approaching its desired size. When this occurs, a yes decision by block 40 brings into play the decision represented by block 43, namely, whether a check of the transpired process time indicates that the round-over portion of the crystal growth process has been completed. If the answer is no," crystal and crucible lift speeds are increased in accordance with predetermined constant increments (block 44) and the next incremental change in heater power for the neck-in phase is calculated as before (block 41).

When the accumulated process time indicates (block 43) that the round-over phase has been completed, the accumulated crystal length is calculated (block 58) and is compared (block 56) with the maximum length of the crystal that can be pulled from the known amount of silicon charge originally placed in the crucible. 1f the comparison indicates that the crystal has reached its maximum length, a yes output from decision block 56 activates block 57 to execute the sprout or withdrawal phase. This is done by incrementing the heater power to increase the melt temperature and prevent the crystal from freezing on the crucible, by gradually restoring the crystal pull speed to its preset nominal value, and by gradually decreasing the crucible rotation speed while incrementally reducing crucible lift speed to zero.

In the event that the decision (block 56) is no," then the computation of block 45 is performed. More particularly, two previous readings from radiation sensor 31 are processed with the following equation to produce a predicted reading (representing crystal diameter) at a projected future time.

I I and I are defined as in equation (2) The above equation, in effect, takes the last two readings from sensor 31 (in a typical case successive readings are taken at l8-second intervals) and linearly projects said two readings to a predetermined future time (for example 36 seconds after the second reading). The linear projection is a simple case of curve-fitting sampled data to determine the data trend. Linear projection has been found to be adequate. More complex nonlinear functions may be used, if desired. The computed-projected diameter reading is stored in the computer memory for later use.

The computer program next calls for the calculation (blocks 46 and 47 of FIG. 4) of an incremental power change to heater ll of FIG. 1 base upon the idealized equation (I) and compensating equation (2) previously described which is added (block 48) to the last heater power set point to provide a new heater power set point. The updated heater power set point then is stored in computer memory for accessing at a later time.

At this point, the calculation ofa new pull speed set point is called for by the program (block 49) utilizing equation (3) previously discussed. The new pull speed is stored in the computer memory for later use. Total melt drop is calculated (block 50) as a prerequisite to making a decision (block 51) as to whether the melt surface is still within the cylindrical portion 32 of the crucible 4 or has fallen to the bottom portion 33 of the crucible where the walls are curved. 1f the melt surface has fallen to the curved region 33 of the crucible, crucible lift speed is determined in accordance with the following This last calculation is represented by block 52 of H6. 5. In the alternative event that the melt surface is still within the cylindrical portion 32 of the crucible, the calculation represented by block 53 is carried out using the following equation:

1 -2 .42 0lt D dt where (in both equations 7 and 8):

dc/dt melt drop rate, inches per hour dx/dt crystal lift speed, inches per hour d= crystal diameter (inches) D= crucible diameter (inches) The calculated new crucible lift speed set point is stored in computer memory for subsequent use. It should be noted that the amount of the melt drop is calculated base upon the known original silicon chargein the crucible before the growth process was started, the known nominal crystal pull rate, and the known elapsed time from the initiation of the growth process.

Following the calculation of the new crucible lift speed (block 52 and 53), all calculated set points are converted into corresponding digital representations of respective process control parameters to be used during the next process time increment. First, the heater power calculation of block 42 previously described is carried out and communicated to a respective digital-to-analog converter for controlling heater 1]. Next, the digital output to each of the motors is calculated (block 54) using the following equation:

nz,, output to motor m last digital output, prior to m,,

e error value S value of set point at V V,, nth reading of tachometer The set points for crystal and crucible rotation typically are fixed values and do not themselves require separate computation. The set points for crystal lift and crucible lift rates were established in blocks 49 and either block 52 or 53. The calculated digital outputs are sent to the corresponding motor controllers via respective digital-to-analog converters.

Following the communication of the various digital outputs to the heater and to each of the four motor controllers, new values representing each of the crystal-growing process variables are sensed and stored (block 55) in the computer memory including heater temperature, crystal pull speed, crystal rotation speed, crucible lift speed, and crucible rotation speed. One new cycle of the program loop then is initiated by entrance into block 37 of FIG. 3.

While this invention has been particularly described with reference to the preferred embodiments thereof, it will be understood by those skilled in the art that the foregoing and other changes in form and details may be made therein without departing from the spirit and scope of the invention.

What is claimed is:

1. In the machine-implemented growth of a crystal by pulling from a melt of semiconductor material, the process for adjusting the temperature of said melt whereby the diameter of the growing crystal is controlled comprising:

machine sensing the diameter of said crystal at predetermined time intervals,

machine computing by curve-fitting technique the projected crystal diameter at a predetermined future time using the sensed crystal diameters,

machine sensing the temperature of said melt,

machine computing a corrected melt temperature using the sensed melt temperature and said projected crystal diameter,

machine comparing said corrected melt temperature with said sensed melt temperature to ascertain the difference, if any, therebetween and machine controlling the temperature of said melt in accordance with said difference.

2. The method defined in claim 1 and further including:

machine computing a corrected pulling rate using a nominal pulling rate and said projected crystal diameter,

machine sensing the pulling rate of said crystal from said melt, machine comparing said corrected pulling rate with the sensed pulling rate to ascertain the difference, if any, therebetween, and

machine adjusting said pulling rate in accordance with said last-named difference.

3. The method defined in claim 1 wherein the diameter of said crystal is machine sensed only along a predetermined radius thereof.

I t I l 

2. The method defined in claim 1 and further including: machine computing a corrected pulling rate using a nominal pulling rate and said projected crystal diameter, machine sensing the pulling rate of said crystal from said melt, machine comparing said corrected pulling rate with the sensed pulling rate to ascertain the difference, if any, therebetween, and machine adjusting said pulling rate in accordance with said last-named difference.
 3. The method defined in claim 1 wherein the diameter of said crystal is machine sensed only along a predetermined radius thereof. 